Abstract
In this paper, we develop a new neural network family based on power series expansion, which is proved to achieve a better approximation accuracy in comparison with existing neural networks. This new set of neural networks embeds the power series expansion (PSE) into the neural network structure. Then it can improve the representation ability while preserving comparable computational cost by increasing the degree of PSE instead of increasing the depth or width. Both theoretical approximation and numerical results show the advantages of this new neural network.
•We develop a new set of neural networks by analogy to a power series expansion.•Theoretical analysis shows that PSENet can achieve a better approximation accuracy than other commonly used neural networks.•The new set of neural networks has been tested on different datasets and its advantages over other neural networks are shown.